Although not intended to be adjustable, the jet will move if you put enough force on it. IMO it shouldn't be necessary though, unless there is something else wrong.
I once fought overheating problems on a TR3A for a long time that eventually turned out to be worn jets. Had SU carbs so not the same as your ZS; but similar. With both carbs, the mixture adjustment actually affects the entire range. So, if some other factor is making it idle rich; and you lean out the jet/needle to correct the idle; the cruise mixture will now be too lean and potentially cause problems. On my Dad's TR3A, it cost him an engine rebuild when the lean mixture finally eroded a valve stem enough to break.